1. Field of the Invention
The present invention relates to a method for evaluating an optical member for an optical element such as a lens and a prism used for the photolithography technique.
2. Description of the Related Art
Exposure apparatuses for the photolithography are used to produce, for example, semiconductor devices such as LSI, liquid crystal display devices, and thin film magnetic heads. In such an exposure apparatus, a light, which is emitted from a light source, is radiated via an illumination optical system onto a pattern formed on a projection master plate such as a mask or a reticle. The pattern, which is irradiated with the light beam, is projected by a projection optical system onto a photosensitive substrate such as a glass plate or a wafer previously applied with a photoresist. The types of the projection optical system include the refractive type projection optical system which is constructed only by lenses for transmitting and refracting the light beam having the exposure wavelength, the reflection type projection optical system which is constructed only by mirrors for reflecting the light beam having the exposure wavelength, and the cata-dioptric type projection optical system which is constructed by lenses and mirrors in combination.
In recent years, the degree of integration is increasingly enhanced, for example, for the semiconductor device, the liquid crystal display device, and the thin film magnetic head. The pattern, which is transferred onto the substrate, is continuously made more fine and minute. Therefore, the wavelength is progressively shortened for the exposure apparatus for the photolithography such that the light source is changed from the i-ray (365 nm) to the KrF excimer laser (248 nm), the ArF excimer laser (193 nm), and the F2 laser (157 nm). Accordingly, higher optical performance is required for the optical system of the exposure apparatus for the photolithography. In particular, extremely high optical performance, in which the resolution is high and the aberration is approximately zero, is required for the projection optical system for transferring the fine and minute pattern on the mask onto the photosensitive surface of the wafer. In order to satisfy the request as described above, an extremely high level is required for the refractive index homogeneity of the optical material (hereinafter referred to as “optical member for the photolithography” as well) to be used, for example, for the lens, the prism, and the photomask as constitutive elements for the optical system of the exposure apparatus for the photolithography. That is, the absence of any nonuniformity (refractive index homogeneity) is important for the optical member for the photolithography.
The refractive index homogeneity of the optical member for the photolithography has been hitherto evaluated as follows. That is, a light beam is allowed to pass through the optical member to measure the wave front aberration generated in this situation. The evaluation is made by using an index such as the difference between the maximum value and the minimum value (hereinafter referred to as “PV value”) and the root mean square (hereinafter referred to as “RMS value”). That is, when the PV value and the RMS value are smaller, the evaluation is made such that the optical member is excellent. Therefore, the optical member, which is regarded to have a high quality, has been produced in order to decrease these values.
Japanese Patent Application Laid-open No. 8-5505 describes a method for evaluating the refractive index homogeneity. An explanation will be briefly made below with reference to FIG. 10 about a specified procedure of this method.    (1) An optical member for the photolithography, which was polished to have a columnar or prism-shaped configuration, is set to an interferometer, and a reference wave front is emitted on the polished surface to measure the wave front aberration. The measured wave front aberration includes any error aberration resulting from the refractive index distribution of the optical member. Therefore, information about the refractive index distribution is obtained by analyzing the aberration. In particular, the error aberration, which results from the curvature component, is referred to as “power component” or “focus component”. Further, the error aberration, which results from the inclination component, is referred to as “tilt component”.    (2) The power component and the tilt component are removed from the measured wave front aberration.    (3) Further, the wave front aberration, which results from the astigmatic component, is removed.    (4) The remaining wave front aberration is separated into the rotational symmetry component and the rotational asymmetry component (random component).    (5) The PV value and the RMS value of the rotational asymmetry component (random component) are determined, and these values are used to make the evaluation.    (6) The rotational symmetry component is subjected to the fitting to the aspherical formula by the least squares method, and the 2nd order and the 4th order components are removed to determine the PV values and the RMS values of the remaining wave front components of the eventh orders of the 6th order or higher orders (hereinafter referred to as 2nd order 4th order residual”. The values are used to make the evaluation. That is, the optical member, in which the rotational asymmetry component (random component) and the 2nd order 4th order residual are small, is the optical member in which the refractive index homogeneity is satisfactory. It has been tried to produce the optical member as described above.
The wave front aberration of the optical member for the photolithography is measured by using the interferometer. Those generally usable as the interferometer include the Fizeau type interferometer for measuring the flat optical member by using a light source of a He—Ne laser having a wavelength of 633 nm. The interferometer has such a structure that a measurement objective is interposed and fixed between two parallel flat plates. The procedure is more faithful to the principle, in which the KrF excimer laser (248 nm) or the ArF excimer laser (193 nm) is used as the light source to be employed for the measurement of the wave front aberration. However, the He—Ne laser is used in many cases, for example, because of the cost of the interferometer, the size, and the measurement stability.
In order to highly accurately measure the wave front aberration of the optical member by using the interferometer, it is necessary to measure the interference light beam while effectively avoiding the scattering of the measuring light beam from the surface of the measurement objective. In order to reduce the influence of the scattering of the measuring light beam, it is desirable to use a method called “oil-on-plate method” in which the optical member as the measurement objective is interposed between the two parallel flat plates, and the gaps therebetween are filled with a transparent oil.
An explanation will be made about a method with reference to illustrative views shown in FIGS. 11A and 11B. At first, the Fizeau type interferometer, which is used for the measurement, is explained. The Fizeau type interferometer is composed of a main body section 21, a reference surface object 22, two parallel flat plates 23, and a reflecting surface 25. Before an optical member 24 as the measurement objective is set to the interferometer, the two parallel flat plates 23 are arranged close to each other, and the gap therebetween is filled with a transparent oil 26 which has approximately the same refractive index as that the measurement objective. In this state, the reference wave front based on the laser beam is radiated to photograph the transmitted light beam, and thus the wave front aberration data is obtained. This state is shown in FIG. 11A. Subsequently, the gaps between the parallel flat plates 23 and the optical member 24 are filled with the transparent oil 26 in a state in which the optical member 24 is set between the two parallel flat plates 23. In this state, the transmitted light beam is photographed to obtain the wave front aberration data. This state is shown in FIG. 11B. Subsequently, the wave front aberration data, which is measured in the state in which the optical member is not set, is subtracted from the wave front aberration data which is measured in the state in which the optical member 24 is set. Accordingly, the influence of the measurement error, which results from the wave front aberration depending on the surface shape of the optical member 24, is removed, simultaneously with which the error caused by the wave front aberration resulting from the interferometer is removed as well to measure only the wave front aberration in the optical member 24. That is, it is possible to determine the wave front aberration inherent in the optical member.
The principle will be explained in detail below. It is assumed that W represents the wave front aberration which depends on the internal homogeneity of the optical member, E represents the wave front aberration which depends on the interferometer, and O represents the wave front aberration which depends on the oil. On this assumption, the wave front measurement data D1, which is measured in the state in which the optical member is set, is expressed as follows.D1=W+E+O  (1)The wave front measurement data D2, which is measured in the state in which the optical member is not set, includes the wave front aberration E depending on the interferometer and the wave front aberration O depending on the oil. Therefore, the wave front measurement data D2 is expressed as follows.D2=E+O  (2)Therefore, when the wave front measurement data D2, which is measured in the state in which the optical member is not set, is subtracted from the wave front measurement data D1 which is measured in the state in which the optical member is set, the following expression is obtained.D1−D2=W+E+O−(E+O)=W  (3)Only the wave front aberration W, which depends on the internal homogeneity of the optical member, is separated and determined.
When the wave front aberration is actually measured, the measurement area is divided into a plurality of measurement elements to obtain measured values for each of the elements. The measured values are connected and combined to thereby grasp the wave front aberration of the entire measurement area. As for the number of the measurement elements, when the cross section is circular, it is desirable that the measured values of the respective elements are obtained in relation to the number of the elements obtained by dividing a square area with the inscribing circle of the circular cross section into not less than 50×50 meshes. It is desirable that the number of the elements (number of measuring points) is changed depending on the diameter of the measurement objective. It is more desirable that the number of the elements (number of measuring points) is determined while considering the light flux diameter (partial diameter) when the lens, which is obtained by processing the optical member, is used as well. For example, in an optical system shown in FIG. 9, the light flux, which has been transmitted through the reticle R, is focused on the surface of the wafer W after passing through lens groups from G1 to G6. In this situation, the light flux diameters (partial diameters) differ in relation to the transmittance through the respective lenses. That is, the lens, which is disposed near to the reticle R, has the light flux diameter which is smaller than the light flux diameter of the lens which is disposed far from the reticle R (near to the wafer W). When the number of the measurement elements is set for the optical member to be used for each of the lenses as described above so that the number of the measuring points in the light flux diameter of the lens is approximately equivalent, it is possible to perform the measurement with approximately equivalent accuracies for the lenses of the plurality of types. In the method in which the number of the measurement elements is set taking the light flux diameter into consideration, if it is intended to perform the measurement comprehensively for the inside of the effective diameter of the lens of the optical member to be used for the lens which has the large effective diameter and which has the small light flux diameter, the number of the measurement elements is extremely large. In such a case, the wave front aberration is measured for each of a plurality of areas of the optical member, and the obtained pieces of the wave front aberration data are combined. Thus, it is possible to obtain the entire wave front aberration data. Those usable for the measurement of the wave front aberration include the Twyman-Green type interferometer and the Shearing type interferometer other than the Fizeau type interferometer as well.
The measured wave front aberration data is dealt with as follows as shown in FIG. 8. That is, the coordinate system is defined on the outgoing pupil plane 80 of the optical member, and the obtained wave front aberration is expressed by using the coordinate system. That is, the polar coordinates are defined on the outgoing pupil plane, and the obtained wave front aberration W is expressed as W(ρ, θ).
Japanese Patent Application No. 2002-162628 describes the following procedure. That is, the transmission wave front data of an optical member is subjected to the Zernike expansion to make separation into the rotational symmetry component, the odd number symmetry component, and the even number symmetry component, and they are further separated depending on the orders into a plurality of portions (lower order, middle order, higher order) so that the evaluation is made in accordance with the respective RMS values. It is also described that the optical member is rotated and laterally shifted, and the transmission wave front data of the optical member is separated into the rotational symmetry component and the rotational asymmetry component.
The interferometer includes the two types, i.e., the type in which the surface, through which the light beam comes into the optical member, is set in the vertical direction (i.e., called “lateral type” because of the horizontal optical axis), and the type in which the surface, through which the light beam comes into the optical member, is set in the horizontal direction (i.e., called “vertical type” because of the vertical optical axis).
In the case of the lateral type, the optical member is set in a standing form. Therefore, the load of the optical member is concentrated on the lower support, and any strain tends to appear in the optical member. Further, the oil, which is charged between the parallel flat plate and the optical member, flows downwardly due to its self-weight. Therefore, any error, which is caused by this fact, tends to be mixed into the measured value. Therefore, the lateral type is not suitable for the highly accurate measurement of the wave front aberration.
Therefore, in order to measure the wave front aberration highly accurately, the vertical type is used. However, in the case of the vertical type, the load of the optical member is received via the oil by the parallel flat plate disposed on the lower side. Therefore, any bending appears in the parallel flat plate disposed on the lower side. Further, the oil, which is charged between the optical member and the parallel flat plate disposed on the lower side, is extruded outwardly to flow due to the load of the optical member. A problem arises such that any error caused by these phenomena is mixed into the measured value.